## power.TOST with logscale=FALSE [General Statistics]

Dear ElMaestro,

» Please explain then what exactly it is that power.TOST calculates when I use logscale=F.

» Does it calculate power for a hypothesis based on a difference or for a ratio?

» Which difference? Which ratio?

Take the reference you mentioned above, Hauschke et al. Statist. Med 1999 and use equation (2) for the hypotheses tested, hypotheses based on the difference µT-µR.

These hypotheses can be reformulated with ratios as written in equation (3) by division with µR and by adding 1. But this then had the implicit constraint that µR has to be >0.

» ...

» I am convinced the assuming theta1=-0.2 by default when logscale=F is a misnomer. theta1 is elsewhere understood as an equivalence margin expressed as a ratio and that can't realistically be negative. If powerTOST tries to emulate Hauschke's paper then -.2 is f1, not a theta.

PowerTOST does not emulate any paper. And it does not use the argument theta1 solely as equivalence margin of a ratio. See the man page of power.TOST() how theta1, theta2 and theta0 have to be set for

But you are right: compared to Hauschke's paper -.2 is f1.

Please consider the rest of the Hauschke paper introducing the Fieller CI as exact method.

» Please explain then what exactly it is that power.TOST calculates when I use logscale=F.

» Does it calculate power for a hypothesis based on a difference or for a ratio?

» Which difference? Which ratio?

Take the reference you mentioned above, Hauschke et al. Statist. Med 1999 and use equation (2) for the hypotheses tested, hypotheses based on the difference µT-µR.

These hypotheses can be reformulated with ratios as written in equation (3) by division with µR and by adding 1. But this then had the implicit constraint that µR has to be >0.

» ...

» I am convinced the assuming theta1=-0.2 by default when logscale=F is a misnomer. theta1 is elsewhere understood as an equivalence margin expressed as a ratio and that can't realistically be negative. If powerTOST tries to emulate Hauschke's paper then -.2 is f1, not a theta.

PowerTOST does not emulate any paper. And it does not use the argument theta1 solely as equivalence margin of a ratio. See the man page of power.TOST() how theta1, theta2 and theta0 have to be set for

`logscale = TRUE`

or `logscale=FALSE`

.But you are right: compared to Hauschke's paper -.2 is f1.

Please consider the rest of the Hauschke paper introducing the Fieller CI as exact method.

—

Regards,

Detlew

Regards,

Detlew

### Complete thread:

- On CI calculation, untransformed metrics ElMaestro 2019-11-29 03:40
- Fieller’s (‘fiducial’) confidence interval Helmut 2019-11-29 10:03
- Fieller’s (‘fiducial’) confidence interval ElMaestro 2019-11-29 15:53
- Fieller’s (‘fiducial’) confidence interval d_labes 2019-11-29 17:20
- Fieller’s (‘fiducial’) confidence interval ElMaestro 2019-11-30 05:11
- power.TOST with logscale=FALSEd_labes 2019-11-30 14:01

- Fieller’s (‘fiducial’) confidence interval ElMaestro 2019-11-30 05:11

- Fieller’s (‘fiducial’) confidence interval d_labes 2019-11-29 17:20

- Fieller’s (‘fiducial’) confidence interval ElMaestro 2019-11-29 15:53
- On CI calculation, untransformed metrics PharmCat 2019-11-29 12:05

- Fieller’s (‘fiducial’) confidence interval Helmut 2019-11-29 10:03